TY - JOUR
T1 - A least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition
AU - He, Qiaolin
AU - Glowinski, Roland
AU - Wang, Xiao Ping
N1 - Funding Information:
This research is supported part by NSFC (No. 11201322 , No. 11671027 ) and Sichuan Science and Technology Project No. 2016JY0196 .
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In this article, we discuss a least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-domains of Rd, with B‾⊂Ω, in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious domain method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above methodology is also provided. Numerical results are given; they suggest optimal order of convergence.
AB - In this article, we discuss a least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-domains of Rd, with B‾⊂Ω, in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious domain method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above methodology is also provided. Numerical results are given; they suggest optimal order of convergence.
KW - Fictitious domain method
KW - Incompressible viscous flow
KW - Least-squares
KW - Navier slip boundary condition
UR - http://www.scopus.com/inward/record.url?scp=85045558343&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.04.013
DO - 10.1016/j.jcp.2018.04.013
M3 - Journal article
AN - SCOPUS:85045558343
SN - 0021-9991
VL - 366
SP - 281
EP - 297
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -